Anharmonic 1D actuator model including electrostatic and Casimir forces with fractional damping perturbed by an external force

We modeled a one-dimensional actuator including the Casimir and electrostatic forces perturbed by an external force with fractional damping. The movable electrode was assumed to oscillate by an anharmonic elastic force originated from Murrell- Mottram or Lippincott potential. The nonlinear equations have been solved via the Adomian decomposition method. The behavior of the displacement of the electrode from equilibrium position, its velocity and acceleration were described versus time. Also, the changes of the displacement have been investigated according to the frequency of the external force and the voltage of the electrostatic force. The convergence of the Adomian method and the effect of the orders of expansion on the displacement versus time, frequency, and voltage were discussed. The pull-in parameter was obtained and compared with the other models in the literature. This parameter was described versus the equilibrium position and anharmonicity constant.

Casimir Force at a Finite Cut-Off

We calculate the Casimir force at a finite cut-off A by summing the forces induced by the all fluctuation modes. We show that the Casimir force is independent of the cut-off function in the limit L∧ → ∞. There is a correction in the order of （L∧）^-2, when L∧ is finite and large. This correction becomes remarkable when L is comparable with the microscopic length scale ∧^-1. It has been demonstrated that the Casimir force at a finite cut-off should be defined by summing forces of all fluctuation modes, instead of the derivative of Casimir energy with respect to L where an additional derivative of the cut-off function has been introduced.

Corrections to the Casimir Force Due to Interactions of Plasmons and Electromagnetic Field

Considering the interaction between the electromagnetic field and matter field, a concise method is used to calculate the ground-state energy of the interacting system. With the assumption of squeezed-like state, a new vacuum state is obtained for the inte racting system. The energy of the new vacuum state is obviously lower than that of unperturbed vacu um state. Based on the new vacuum state, the correction to the Casimir force is obtained. The r esult shows that the contribution of the interaction is a repulsive one and the Casimir effect is attributed to both electromagnetic field and matter field. On the basis of the obtained results, th e recent experimental data can be explained reasonably.

Casimir Force on a Piston in Randall-Sundrum Models

The Casimir effect of a piston for massless scalar fields which satisfy Dirichlet boundary conditions in the context of five-dimensional Randall- Sundrum models is studied. In these scenarios we derive and calculate the expression for the Casimir force on the piston. We also discuss the Casimir force in the limit that one outer plate is moved to the remote place to show that the nature of the reduced force between the parallel plates left. In the Randall^undrum model involving two branes the two plates attract each other when they locate very closely, but the reduced Casimir force turns to be repulsive as the plates separation is not extremely tiny, which is against the experimental phenomena, meaning that the RSI model can not be acceptable. In the case of one brane model the shape of the reduced Casimir force is similar to that of the standard two-parallel-system in the four-dimensional fiat spacetimes while the sign of force remains negative.

Isotope effect on the Casimir force

Isotopic dependence of the Casimir force is key to probing new physics and pushing novel technologies at the micro and nanoscale, but is largely unexplored. In 2002, an isotope effect of 10^(-4) was estimated for metals—orders of magnitude beyond the experimental resolution. Here, by employing the Lifshitz theory, we reveal a significant isotope effect of over 10^(-1) for polar dielectrics. This effect arises from the isotope-mass-induced line shift of the zone-center optical phonons and is insensitive to the linewidth. We perform numerical analyses on both the imaginary and real-frequency axes, and derive analytical formulas for predicting the isotope effect. The three-orders-of-magnitude difference between polar dielectrics and metals arises from the distinct isotopic dependence of the phonon and plasma frequencies. Our work opens up a new avenue for engineering forces at small scales and may also facilitate the quest for the fifth force of nature.

Repulsive Casimir Force in a Cavity Comprising a Dielectric with Output Coupling

The Casimir force between a perfectly conducting wall and a dielectric wall in a cavity comprising a transparent dielectric with output coupling is investigated. By using furl quantum theory, we obtain the analysis expression of the force, which shows that the interaction of the two walls in this system is always repulsive. And the value of the Casimir force varies with the field amplitude reflectivity and the cavity size.

Casimir Force Correction Between Parallel Polysilicon Plates

Both the size of the components and the separation between them in some microelectromechanical systems (MEMS) are already in the sub-micrometer regime, where quantum mechanical effects such as the Casimir effect will need to be considered. This paper theoretically analyzes the roughness, electrical conductivity, and temperature corrections due to the Casimir force between two parallel polysilicon plates. The theoretical results show that the combined effects of roughness, conductivity and temperature cause a maximum relative error of the Casimir force per unit area of 26.2% between parallel polysilicon plates separated by 1 μm. Therefore, the surface roughness and finite conductivity corrections should be taken into account when calculating precise Casimir forces with separations on the order of 1 μm.

Casimir Force in a One-Dimensional Cavity with Quasimode

We calculate the Casimir force between a perfect reflective wall and a semitransparent wall in the laser cavity. Using the Fox–Li quasimode theory to describe the electromagnetic field in the laser cavity, the vacuum energy and the Casimir force are calculated. We compare our results to the force in the ideal situation and find it smaller in the dissipative cavity. We also find that the Casimir force decreases with the increase of the wall-wall distance and the decay rate of the quasimodes in the laser cavity.

Shape of Compact Toroidal Dimensions T_θ~d and Casimir Effect on M^D×T_θ~d Spacetime

We study the influence of the shape of compact a scalar field. We examine both the massive and the massless dimensions to the Casimir energy and Casimir force of scalar field. The total spacetime topology is M^D × Tθ2, where M^D） is the D-dimensional Minkowski spacetime and Tθ2 the twisted torus described by R1, R2, and 8. For the case R1 = R2 we found that the massive bulk scalar field Casimir energy is singular for D=even and this singularity is R-dependent and remains even when the force is calculated. Also the massless Casimir energy and force is regular only for D = 4 （!）. This is very interesting phenomenologically. We examine the energy and force as a function of 8. Also we address the stabilization problem of the compact space. We also briefly discuss some phenomenological implications.

Quantitative Structure-activity Relationship for Heterogeneous Phenol Compounds Using Zero Point Energy

The calculations of quantum mechanical descriptors of 79 heterogeneous phenol compounds were presented at the HF/6-31G＊ and B3LYP/6-31G＊ levels of theory.Quantitative structure-activity relationship（QSAR） models of the growth inhibition activity（pIGC50） of 79 heterogeneous phenols were established using some of the following calculated quantum mechanical descriptors：the zero point energy（ZPE）,the front-line orbital energy（EHOMO,ELUMO）,the differences between HOMO and LUMO energies（ΔE）,and the molecular dipole moment（μ）.The QSAR models obtained by employing multiple linear regression techniques are aimed at correlating the structures to their experimental pIGC50.The most significant is a one-parameter linear equation with the correlation coefficient R2 values to be 0.855（HF） and 0.844（B3LYP）.The results display that the zero point energy as a special quantum-chemical descriptor in the QSAR equations indicates the existence of Casimir force in the interaction between the molecules of compounds and biological receptor（cells）.The physical mechanism of structure-activity of the molecules at a deeper level would have a new understanding.

Pull-in instability analyses for NEMS actuators with quartic shape approximation

The pull-in instability of a cantilever nano-actuator model incorporating the effects of the surface, the fringing field, and the Casimir attraction force is investigated. A new quartic polynomial is proposed as the shape function of the beam during the deflection, satisfying all of the four boundary values. The Gaussian quadrature rule is used to treat the involved integrations, and the design parameters are preserved in the evaluated formulas. The analytic expressions are derived for the tip deflection and pull-in parameters of the cantilever beam. The micro-electromechanical system （MEMS） cantilever actuators and freestanding nano-actuators are considered as two special cases. It is proved that the proposed method is convenient for the analyses of the effects of the surface, the Casimir force, and the fringing field on the pull-in parameters.

On the Cosmical Zero Point Energy Density

The frequency spectrum of the cosmical Zero Point Energy (ZPE) and its total density are so far unknown in their details. In the present complementary investigation, a revised theory forms the basis for studies of this concept in two respects. It first applies to the observable universe considered as an entity, as well as to included subregions such as the galaxies with supermassive black holes. Second, experiments are proposed on the maximum Casimir force arising between two metal plates of different materials and with a vanishing air gap in their spacing. This serves the purpose of making an indirect determination of the ZPE energy density in the laboratory, i.e. at the Earth’s orbit. The ZPE energy density is interpreted as dark matter density and its pressure gradient as dark energy force density.